| Since hundred years ago, when Roentgen discovered x-rays, medical imaging and surgical visualization has revolutionarily developed. Medicine knowledge, physics concept, mathematics method and computer science have interdisciplinarily worked together on the medical image processing and graphics computation. It has been the long term dream of the computer scientists to simulate the medical reality and its relevant computer system. In recent years, the 3D modeling of human organic soft tissue deformation has been an important research in computer graphics. The soft tissue modeling is basic module for the real-time simulation and human computer interaction.In this paper, we discuss the virtual surgical system, including its software requirements and algorithms modules analysis. Especially, the application of deformation modeling in the virtual surgery system is emphasized and analysized in a key framework. As for deformation models, traditional mass-spring algorithm is discuessed. It models the deformable object as the network of masses and springs. Its computational complexity is low but it is limited in accuracy. The traditional finite elements method is also introduced, which is a high accuracy numerical analysis method with complex computation. And we discuss a latest algorithm, medial representation. It rebuilds the surface based on the centerline information to model the deformation from internal structure to surface mesh. Because medical data visualization is the precondition for soft tissue modeling, we introduce the relating contents of 3D meshing, image segmentation, etc.Real-time surgical simulation and animation of soft tissue deformation, using linear elastic mass-spring or traditional finite element method, is difficult to achieve the high efficiency and quality due to the following reasons: (1) linear elastic model is inappropriate for simulating large deformation for unreasonable distortion; (2) complexity of 3D problem, the number of elements in the model mesh is at least one dimension larger than a 2D magnitude; (3) medial representation loses regional deformation details.In this research, we model and simulate large global deformations of human soft-tissue for virtual surgery system, employing the hybrid models of finite elements, mass-spring and, especially, medial representation. We propose a novel approach to address problems: (1) Employing novel deformable models of medial supportive structure and medial representation, we apply the hybrid deformable model, by finely calculating the volumetric deformation in the local region while simply calculating the global deformation by medial representation method. Experiments have been given to show the feasibility and efficiency of the model; (2) To achieve the real-time requirement of realistic deformable modeling, it is necessary to use the Graphics Processing Unit parallel computing for Finite Elements Model on regional deformation details, so that the major calculation work in the conjugate gradient solver for the solution matrix is moved from Central Processing Unit to Graphics Processing Unit to accelerate the effectiveness.Dynamic global deformation of elastic objects was implemented using Deformable Medial Structure with its representative meshes. On a 2.80 GHz P4 PC with 1.0 G memory, and a GeForce-6800 graphics card, a medial structure of 190 elements and a surface mesh of 3250 elements cost approximately 0.05 second per frame, as real-time requirement. Experiments are based on cases of kidney, craniofacial, blood vessel, breast surgeries.We also discuss modeling evaluation based on biset matching algorithm and statistics method. In addition to 3D modeling, we also introduce the issues including force feedback, collision detection, and real-time performance. |
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